What is the probability of flipping a coin 75 times and getting tails 35 times or fewer? round your answer to the nearest tenth of a percent. a. 99.7% b. 32.2% c. 5.3% d. 75.6%

Let X be the number of tail when a coin is flipped n number of times. Let n is the number of times a coin is flipped. Let p be the probability of getting tail on any flip of coin.

Here as coin is fair coin the chance of getting head or tail at any flip is 1/2.

n=75, p =0.5

From given information X follows Binomial distribution with n=75 and p=0.5

The probability that getting tail 35 or fewer times is

P(X ≤ 35) = P(X=35) + P(X=34) + P(X=33) + ....+ P(X=2) + P(x=1)

The Binomial probability is calculated using probability function

For given parameters n=75 and p=0.5 the probability of getting X=k is

Using excel function to find cumulative binomial probability for x=1 to 35 is

=BINOM.DIST(35,75,0.5,1) = 0.322

The probability there will be 35 or fewer tails is 0.322

The percentage of getting 35 or fewer tails is 32.2%